Question

Using rational approximations, what statement is true?
√49>7


√49<7
√48>√36


√48<√36

Answer 1

are you sure

Answer 2

To evaluate the statements, let's analyze each one carefully:

1. **√49 > 7**:
- We know that √49 = 7. Therefore, this statement is false.

2. **√49 < 7**:
- Since √49 = 7, this statement is also false.

3. **√48 > √36**:
- We know that √36 = 6. To find √48, we can recognize that √48 is approximately √(4×12) = 2√12. The value of √12 is around 3.464, so 2√12 is approximately 6.928. Since 6.928 > 6, this statement is true.

4. **√48 < √36**:
- Given that √48 > 6, this statement is false.

From the analysis above, the true statement is:

**√48 > √36**.

Answer 3

Let's carefully reevaluate the comparisons to ensure accuracy.

1. **√49 > 7**:
- √49 = 7, so this is **false**.

2. **√49 < 7**:
- Again, since √49 = 7, this is **false**.

3. **√48 > √36**:
- We know that √36 = 6. Now for √48, we can simplify it to:
\[
\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}
\]
- We know that √3 is approximately 1.732. Therefore,
\[
4\sqrt{3} \approx 4 \times 1.732 \approx 6.928
\]
- Since 6.928 > 6, this statement is **true**.

4. **√48 < √36**:
- This is the opposite of the prior statement, and since we've established that √48 > √36, this is **false**.

So, to confirm, the statement that is true is indeed:

**√48 > √36**.

Thank you for your patience, and the conclusion remains accurate.